Robust H∞/D-stability control of systems with polytopic uncertainty

In this paper, new separated H_∞ performance criterion and D-stability criterion are derived. When used in robust synthesis for real polytopic uncertainty, they can reduce conservativeness inherent in the classical quadratic method by providing a parameter-dependent Lyapunov function, and therefore, lead to potentially less conservative results. The results are then extended to design H_∞/D-stability controllers for polytopic uncertain systems. All the conditions are given in terms of linear matrix inequalities (LMIs). Numerical examples are given to illustrate the proposed method.